Kate and Christopher Hollis are furious that a coroner ruled that their son Tommy's death the day before his first birth was an accident.
Engineer Kevin Elmore admitted mistakenly sawing through the lamp post that killed Tommy, thinking it was an old tramline.
Tommy was crushed in his buggy as his nanny pushed him across a road near construction works in Chiswick, west London.
Kate and Christopher accused coroner Elizabeth Pygott of 'compounding their grief' by banning their lawyer from asking key questions, calling council witnesses or cross-examining the workman.
They had asked Mrs Pygott to give the jury the option of an unlawful killing or open verdict.
But the coroner said the only possible verdict was accidental death because there was not enough evidence to support anything else.
Engineer Mr Elmore told the inquest he wished he could have died instead of Tommy. He was excused from answering questions and left in tears.
The inquest heard workmen were under pressure from Hounslow council to complete a road project.
Tommy's mum, Kate, 40, said: "We did not expect our anguish to be compounded by the coroner's decision to exclude questions and evidence that may lead us to understand better how Tommy was killed."
A lawyer for the couple said: "Legal action will be pursued against those responsible for the death of Tommy Hollis."